Answer:
[-2, 7) ∪ (7, ∞)
Step-by-step explanation:
Given function is,
f(x) = [tex]\frac{0.1\sqrt{4x+8} }{x-7}[/tex]
This function is defined only when
[tex]4x + 8 \geq 0[/tex] [Since square root of a number is not defined]
4x ≥ -8
x ≥ -2
And denominator is greater than of equal to zero.
(If the denominator of a fraction is zero, fraction is not defined)
x - 7 ≥ 0
x ≥ 0
Therefore, domain of the given function will be,
[-2, 7) ∪ (7, ∞)
